Question

Please help :( 2 questions..

If c(x)=5/x-2 and d(x)=x+3 what is the domain of (cd)(x)?

And, if f(x)=7+4x and g(x)=1/2x, what is the value of (f/g)(5)?

Answer 1

For the second one, \[(f/g)(x)=\frac{ f(x) }{ g(x) }\] and you need to evaluate; \[(f/g)(5)= \frac{ f(5) }{ g(5) }\] what you think would be the next step?

Answer 2

also for the 1st question, you seem to have made a "typo", you provided two functions "f(x)" and "d(x)" but it's (cd)(x)?

Answer 3

Oh yes my mistake, first one I meant to put c(x).

And for the second one, what happened to the first equation? f(x)=7x+4

Answer 4

for the second one, just divide the two functions and substitute value of "5" in place of "x",

Answer 5

\[\frac{ f(x) }{ g(x) }=\frac{ 7+4x }{ \frac{ 1 }{ 2 }x}\] and now just substitute the value "5"

Answer 6

Which one is it? \[g(x)=\frac{ 1 }{ 2 }x\]or \[g(x)=\frac{ 1 }{ 2x }\]

Answer 7

First

Answer 8

Ohhh!!! 27/10?

Answer 9

No, first simplify\[\frac{ (7+4x) }{\frac{ 1 }{ 2 }x}=\frac{ 2(7+4x) }{x}\]

Answer 10

Now you can substitute in "5".

For the first one, what you think we have to do?

Answer 11

I got 54.. my gosh i'm so confused..

Answer 12

\[\frac{ 2(7+4(5)) }{ 5 }=\frac{ 2(7+20) }{ 5 }=\frac{ 2(27) }{ 5 }=\frac{ 54 }{ 5 }\]

Answer 13

I'm guessing you multiply after? I did that and got 270. That's one of the answer choices..

Answer 14

is (54/5) in the choice?

Answer 15

Nope! :o

Answer 16

Can you please post the choices?

Answer 17

11/2
27/10
160
270

Answer 18

It seems like \[g(x)=\frac{ 1 }{ 2x }\]and not\[\frac{ 1 }{ 2 }x\]

Answer 19

It is the first one. Did I not say that? ;o

Answer 20

Oops my mistake

Answer 21

\[(f/g)(x)=\frac{ (7+4x) }{ \frac{ 1 }{ 2x } }=\frac{ 2x(7+4x) }{ 1 }=2x(7+4x)\]

Answer 22

Now if you substitute "5" in the function, you get "270"

Answer 23

Yeah. I got it. Thank you so much.

Answer 24

For the 1st one, what you think we have to do?

Answer 25

I have no clue, but it's fine. One last question though. is f(4)+g(4) equivalent to (f+g)(4)?

Answer 26

\[(cd)(x)=[c(x)*d(x)](x)\]

Answer 27

same concept, before we divided two function and now we multiply them.

Answer 28

Yes, it is equivalent.

Answer 29

\[(f+g)(4)\] is same as adding two function and substituting "4" which will give the same result of \[f(4)+g(4)\] which is evaluating for f(4) and g(4) separately and then adding the results together.

Answer 30

Great! You should be my tutor from now on. Such a great help. ;*

Answer 31

One more :( lol

If a(x) and b(x) are linear functions with one variable, which of the following expressions produces a quadratic function?

A.(ab)(x)
B.(a/b)(x)
C.(a – b)(x)
D.(a + b)(x)

C right?

Answer 32

For the first one;\[[c(x)*d(x)](x)=\frac{ 5 }{ (x-2) }*\frac{ (x+3) }{ 1 }=\frac{ 5(x+3) }{ (x-2) }\]and since we can't have division by zero and if we input "2" we get "0" in denominator, therefore \[x>2\]and\[x<2\]
DOMAIN means all the values of "x" which we can input and which gives a logical answer.

Answer 33

"A. (ab)(x)" because if you multiply you linear function e.g. (x*x) you get \[x^2\]which is of degree "2" (Quadratic)

Answer 34

Thanks again. I think I'm done with math for tonight. My brain is going crazy.

Answer 35

\[x^1=x\]is a linear function,
\[x^2\]is a quadratic function.

Answer 36

My pleasure, have a good night.